A; The good news is that your boyfriend understands that he has “issues” and that he needs some help getting over them if he is to be a good partner for anyone. The hard decision for you to make is whether there is enough good in this relationship to be patient and see what comes of it. His therapy isn’t going to be a quick fix. It is going to take some time. If he talks to you about what he is learning and makes some observable changes, he may be serious. If you do stay in this, I suggest that you be included in the therapy sessions now and then. If he is part of a couple, his problems affect you as well as him.
Then it’s a matter of forgiveness. Forgiving someone and trying again is a gift. Once he makes changes, there is nothing else he can do to reassure you or to further earn a second chance. You need to decide if you can genuinely do it. If not, it’s better to wish him well on his personal journey and let go. You don’t want to live your life always suspicious and distrustful of the man you are with. He can’t live his life always under a microscope. It’s not fair to either of you.
But if he’s truly a fine person in every other way and you can forgive and move on, then it’s worth a try.
I wish you well.